证明:(1)∵AC、BD为正方形ABCD的对角线
∴AC⊥BD
又CC′为正方形的高,
∴CC′⊥BD
∵AC∩CC′=C
∴BD⊥面AA′C′C
∵BD∉面AA′C′C且BD∈面BB′D′D
∴面AA′C′C⊥面BB′D′D
(2)∵AC⊥BD,AC⊥BB′且BD∩BB′=B
∴AC⊥面BDD′B′
∵AC∉面BDD′B′且AC∈面ACFE
∴面ACFE⊥面BDD'B
(3)∵AC⊥BD,AC⊥BB′且BD∩BB′=B
∴AC⊥面BDD′B′
∵AC∉面BDD′B′且AC∈面ACG
∴面ACG⊥面BDD'B